I have the following second order ODE:
$$\dfrac{d^{2}r}{dt^{2}}=-2\sin^{2}(\theta)\dfrac{dr}{dt}$$
Where both $r$ and $\theta$ are functions of t (they are polar coordinates). I have been trying to find an explicit solution for , with little success. I have tried using a reduction of order but then get stuck trying to make it explicit. Any suggestions? Thanks.